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Re: Re: Re: Re: Re: How to get an answer as a Root object?

On 22 May 2005, at 13:14, Daniel Lichtblau wrote:

> The variable ordering underlying method 2 is undocumented but hardly
> accidental. While the literature on handling (nonpolynomial)  
> algebraics
> is, I think, a bit scant, there is some folklore to this, and the
> cognoscenti would not regard that approach as a hack. In essence
> approach (3) is equivalent to approach (2), with (for purposes of this
> problem) a small improvement. In making new variables "by hand" we can
> force the ordering. This is advantageous insofar as we can eliminate
> numeric algebraics as well as the other ones. I may at some point  
> try to
> remedy the obscurity of Mathematica GroebnerBasis handling of  
> algebraics
> by adding a remark to the appropriate advanced documentation.

I did not mean to suggest that this behaviur was accidental and I  
realised that it was essentially equivalent to method 3. I used the  
word "hack" in a sense that I once learned on this list form David  
Withoff (who used it once to refer to something in my posting), by  
which I think he meant something relying on undocumented features  
that may equally well not have been there (and may not be there in a  
future implementation). Obviously this feature is undocumented. That  
it "might not have been there"  seems to me to be sufficiently  
demonstrated by the fact that none of the two other programs that  
compute Groebner bases that I have checked do that(or at least not  
when one uses the command "Groebner basis). If not exactly a hack  
then at least this involves some abuse of nomenclature.

Andrzej Kozlowski

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